The purpose of this study is to evaluate the safety and efficacy of combining the chemotherapy drug etoposide with a new chemotherapy drug, paclitaxel, in participants with extensive small cell lung cancer. Both agents, etoposide and paclitaxel have been demonstrated to have independent ability to have activity and lead to tumor shrinkage in patients with extensive small cell lung cancer. This combination of drugs have been shown to be safe and tolerable in patients with other tumor types. An abstract with the clinical results of the study was submitted to the 1998 ASCO (American Society of Clinical Oncology); the listed first author is not the principal investigator, due to limitations by ASCO to have first authorship only in one meeting abstract per year. The abstract is published in Proc Am Soc Clin Oncol 17:474A, 1998. The enrollment in the pharmacokinetics portion of the protocol has been much slower than anticipated, meetings regarding feasibility of completing this translational portion of the study have been ongoing (with Drs. Marks, Reid, and O'Connell). The study remains open for patient accrual.